Solve for $x$ and $y$ using elimination. ${-x+2y = 5}$ ${x-5y = -23}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-3y = -18$ $\dfrac{-3y}{{-3}} = \dfrac{-18}{{-3}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x+2y = 5}\thinspace$ to find $x$ ${-x + 2}{(6)}{= 5}$ $-x+12 = 5$ $-x+12{-12} = 5{-12}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {x-5y = -23}\thinspace$ and get the same answer for $x$ : ${x - 5}{(6)}{= -23}$ ${x = 7}$